Question

The following equation is a quadratic equation.

$(x+2{)}^3=x^3-4$

• A. True
• B. False

Answer 1

The correct option is A True

$(x+2{)}^3=x^3-4$

$x^3+3\left(x^2\right)\left(2\right)+3x(2{)}^2+(2{)}^3=x^3-4$

$x^3+6x^2+12x+8-x^3+4=0$

$6x^2+12x+12=0$

$6(x^2+2x+2)=0$

$\Rightarrow$ $x^2+2x+2=0$

$\Rightarrow$ A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared.

$\Rightarrow$ Comparing equation $x^2+2x+2=0$ with standard form of quadratic equation $a{x}^2+bx+c=0$.

$\Rightarrow$ We get, $a=1,b=2$ and $c=2$

$\therefore$ The equation $(x+2{)}^3=x^3-4$ is quadratic equation is true.